You are forgetting to use SPI library's transfer() function: it takes a byte argument and actually sends it over the SPI bus. You can specify more arguments, namely what to do with SS pin, but this doesn't seem to concern you.
The Arduino SPI EEPROM example might also be useful.
To chop up some data into 8-bit chunks probably the best way is to treat it as a sequence of bytes:
byte data[] = {0x00, 0x00, 0x00, 0x00}; // this is 24 bits (8bits/byte * 4 bytes)
// Transfer 24 bits of data
for (int i=0; i<4; i++) {
transfer(data[i]); // Send 8 bits
}